4/5k-6=7-1/2k

Solution for 4/5k-6=7-1/2k equation:

4/5k-6=7-1/2k

We move all terms to the left:

4/5k-6-(7-1/2k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

4/5k-(-1/2k+7)-6=0

We get rid of parentheses

4/5k+1/2k-7-6=0

We calculate fractions


8k/10k^2+5k/10k^2-7-6=0

We add all the numbers together, and all the variables

8k/10k^2+5k/10k^2-13=0

We multiply all the terms by the denominator


8k+5k-13*10k^2=0

We add all the numbers together, and all the variables

13k-13*10k^2=0

Wy multiply elements

-130k^2+13k=0

a = -130; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-130)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-130}=\frac{-26}{-260}
=1/10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-130}=\frac{0}{-260}
=0
$